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But the crucial point is that since there are only k n - 1 nodes in the network, then if any infinite path is possible, there must be such a path that visits the same node and thus repeats itself after at most k n - 1 cells.
But in practice methods based, for example, on genetic programming seem to do at best only about as well as all sorts of other methods discussed in this chapter.
Indeed, it seems that the best approach is essentially just to search through many different partial differential equations, looking for ones that turn out to show complex behavior.
But regardless of the purpose, the best first step will certainly be to read as much of this book as possible with care. … At first the best thing is probably just to repeat some of the experiments I describe in this book—using the software and resources described at the website, or perhaps just by typing in some of the programs in these notes.
He argued that the best scientific model is one that minimizes this complexity—which with probabilities 0 and 1 is equivalent to minimizing the number of nodes in the network.
In my experience, however, the way to have the best chance of discovering new phenomena in a computer experiment is to make the design of the experiment as simple and direct as possible.
And this means that any issue based on discussing explicit digit sequences for numbers—and whether for example they are simple or complicated—tends to seem at best bizarre.
Yet for quite a few years, this rather unsatisfactory type of statement has been the best that one could make.
For one might think that microscopic physical processes would always produce the best possible randomness.
But despite this, my strong suspicion is that of all the examples of complex behavior that we see in nature almost none can in the end best be explained in terms of constraints.